10 IMSC, 20-24 August 2007, Beijing Page 1 An assessment of global, regional and local...

10 IMSC, 20-24 August 2007, Beijing

An assessment of global, regional and local record-breaking statistics

in annual mean temperature

Eduardo Zorita1 and Hans von Storch12

1Institute for Coastal Research, GKSS Research Center, Geesthacht, Germany

2Meteorological Institute, Hamburg University, Hamburg, Germany

and Thomas StockerClimate and Environmental Physics, Physics Institute, University of Bern ,

Switzerland

10 IMSC, 20-24 August 2007, BeijingPage 3

Among the last 16 years, 1991-2006, there were the 12 warmest years since 1881 (i.e., in 126 samples) – how probable is such an event if the time series were stationary?

Global analysis


How probable is the event

E = at least 12 of the largest values of a sequence of 126 random numbers are among the last 16 samples

given that the generating process X is stationary?


a) X is a “short memory” process, e.g., AR(1) with an exponentially decaying covariance functions (k) = -k

b) X is a “long-memory” process with a power-law decaying auto-covariance function (k) = k-(1+2d), with d being named fractional differencing parameter.

drawn from a distribution

with mean 0.7 and stdev 0.4

1+2d drawn from a distribution with mean 0.5 and stdev 0.18

Assumed autocorrelation functions of stationary series


Best guesses

0.8

d 0.3 (??)

d

Prob(E|,d)

AR-1

long-memory

Global analysis


As a further test of the consistency of our result, we found that E never emerges in a historical model simulation during the pre-industrial period 1000-1850.

Global analysis


Extending this type of analysis to regional and local scales

Less record-breaking years (-)

Lower-autocorrelation (+)

Longer time series (+)

… so far only AR(1) simulations


Giorgi-regions

Top: AR(1)-memory

Bottom: Number N of years in 1991-2006 with annual temperature T larger than maximum prior to 1991 (different time series lengths in different regions!)

Regional analysis


5%-significant

Regional analysis


Local analysis: prior to 2001

Temperature series at European stations as described by CRU – AR(1) coefficients


5%-significant



The anthropogenic warming on the global scale has been demonstrated using sophisticated statistical techniques since the mid 1990s. Since then the anthropogenic signal has strengthened, and straightforward probability arguments suffice to demonstrate the presence of non-stationary developments.

The probability of finding the 12 warmest years among the last 16 years in a sequence of 126 years is extremely small, even if different, conservative assumptions concerning the long-term memory of the climate system are taken into account.

Even for local and regional annual mean temperatures, the clustering of recent warmest years is inconsistent with the notion of stationarity. This “success of detection” is due to a blending of strength of signal + length of record + strength of memory.

Conclusions


Generation of synthetic series with long-range-correlation is based on the Fourier Transform. A power-law decaying autocorrelation function is associated with a certain spectral density, which can be calculated analytically.

Realizations of random Gaussian white noise are first Fourier-transformed, and the Fourier coefficients are then modified to achieve the desired spectral form. An inverse Fourier transformation yields a time series with the desired form of the autocorrelation function.

10 IMSC, 20-24 August 2007, Beijing Page 1 An assessment of global, regional and local...

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